What question did this study set out to answer?

The aim is to identify irreducible polynomial SL2 representations that can be lifted to a different modular setting.

April 17, 2026Open Access

Lifting polynomial representations of SL₂(pr) from p to ℤ/psℤ

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The aim is to identify irreducible polynomial SL2 representations that can be lifted to a different modular setting.
Characterization of irreducible polynomial SL2(p^r) representations.
Analysis of lifting conditions to Z/p^sZ for s > 1.
Comparison of indecomposable SL2 representations.
Most irreducible polynomial SL2(p^r) representations do not lift to Z/p^sZ for s > 1.
Two related indecomposable SL2(p^r) representations cannot be lifted to Z/p^sZ representations.

Implication

This work describes polynomial representations of SL2 that lift to Z/p^sZ, indicating limited instances of this behavior.

Abstract

We describe all of the irreducible polynomial pSL2(pr) representations which lift to (ℤ/psℤ)SL2(pr) representations for s > 1, observing that they almost never do. We also show that two related indecomposable pSL2(pr) representations cannot be lifted to ℤ/psℤ representations for s > 1.

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Cite This Study

Parker et al. (2025) studied this question.

synapsesocial.com/papers/69e1ceaa5cdc762e9d857b24 https://doi.org/10.1090/proc/17599

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Implication

This work describes polynomial representations of SL2 that lift to Z/p^sZ, indicating limited instances of this behavior.

Lifting polynomial representations of SL₂(pr) from p to ℤ/psℤ

Key Points

Implication

Abstract

Discussion

Cite This Study

Lifting polynomial representations of SL₂(pr) from p to ℤ/psℤ

Key Points

Implication

Abstract

Discussion

Cite This Study

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